The ultimate goal of seismics is to find the elastic properties of the subsurface. Seismic energy in the form of compressional or shear waves is transmitted into the ground, and the reflections (echoes) from structures in the subsurface are recorded by sensors (hydrophones or geophones) most commonly located at, or near, the surface of the earth.
The wavefield recorded by the sensors is then processed in computers. The resulting “sound images” of the subsurface are interpreted by geophysicists and geologists to make maps of the reflecting structures. These structures are interpreted as interfaces (reflectors), which are reflecting because separating layers with different elastic properties. Such elastic property changes might indicate rock variations and other geological/petrophysical features, which in turn could indicate possible oil/gas traps.
The “sound images” obtained after data processing are also called migrated sections or migrated images. They can be obtained with a vertical axis in time (time migration) or in depth (depth migration). Time migration is a quick and simple processing, leading to seismic sections which might be directly interpreted by geologists in case of rather simple and flat structures. The ultimate goal is however to produce depth migrated sections to assure a more correct and accurate mapping of the reflecting structures.
The most classic processing sequence consists of first reducing the number of data by summing (stacking) nearby records (traces) after some corrections to compensate for different apertures (offsets) between the omission point (source) and the recording one (receiver). The data are then called poststack and can be time- or depth-migrated. To avoid too restrictive assumptions when stacking before processing, the data may also be kept as they are, i.e., with various offsets, and are than called prestack. There again, time- or depth-migration can be performed.
Elastic waves generated by artificial sources, such as those used in oil exploration, and propagating through the earth down to several kilometers, have limited capacities to distinguish small-scale structures. Their “detection power” (resolution) is controlled by different parameters such as the frequency band of the emitted signal, the propagation velocity of the waves, the geometry of the emitting/receiving system (survey) and the earth structure through which the elastic waves propagate.
Due to limited resolution, both across the reflectors and laterally, the migrated sections should be interpreted carefully. They represent a filtered version of the earth structure, with blurred reflectors and possible coherent artifacts not associated with actual reflectors. In addition, not all the reflectors are properly illuminated depending on the geometry of the survey and the way waves propagate in complicated earth structures. It is therefore interesting to control the migrated sections, either prior to the acquisition in order to define the best geometry (aperture and samplings) or after, i.e., at the interpretation level.
The only way to systematically test migration in realistic earth structures is per today to generate synthetic data and use them in the processing sequence. So, in addition to the cost of generating those data, the processing cost will be the same as for real data Moreover, no modeling technique is perfect, and their inherent limits might prevent their use.
Ray tracing methods can calculate synthetic data rather quickly, for chosen reflectors, but might also suffer from the high-frequency limit inherent in the method. Missing reflected events and possibly overestimated amplitudes at caustics might generate disturbing noise on the migrated sections. In opposition to ray tracing methods, the finite-difference modeling techniques, acting as black-boxes, will give all kind of waves, i.e., realistic traces. But the cost of this modeling is extremely high (executing time and memory requirements), especially in 3D models. In any case, synthetic data modeling will require expert users and is seldom used at the interpretation stage.
As a simple alternative to complicated modeling of data based on solving the wave propagation equations, ID-convolution is a technique much in favor, especially in the production groups of oil companies and contractors. This technique solves all easy case in earth modeling: primary reflections in the zero-offset case (poststack data) in a stack of horizontal, flat and homogeneous layers. The so-called “impulse-response” of the earth, i.e., a trace with just “spikes” at the different arrival times of the primary reflections, proportional to the reflecting strength (reflectivity) of each reflector, is convolved with a chosen pulse. The ID convolution method is fast and gives a rather good idea of the vertical resolution, i.e., if close reflectors in time/depth are detectable. But a stack of horizontal, homogeneous layers is usually a poor model of the earth and will not properly describe the actual 2D/3D heterogeneity of the structures and its implications on wave propagation.
The current patent application describes a new method which efficiently simulates prestack depth migrated sections without generating synthetic data to be used in the classic processing seismic sequence. A background model is required for ray tracing and equivalent methods but there is no need for detailed structure information in the target zone. The latter will, on the contrary, be sort of a variable in the process, i.e., several target models can be simulated with the same background model. Still with the same background model, various survey geometries and sub-selections, as well as various pulses, can be tried and the output will be simulated prestack depth migrated sections for each (target model, survey, pulse) case. Various applications of the method have been identified in important areas such as survey planning, interpretation, prestack depth migration (PSDM) and AVO/AVA analyses. The method is not restricted to seismic applications (oil exploration or shallower/deeper investigations) but covers all case of wave propagation similar to the elastic wave case. Potential applications in, for instance, Ground Penetrating Radar (GPR), have been already tested, and other applications could be in acoustical and medical imaging. An extension of the invention is also the generation of simulated seismic data. i.e., time recordings of seismic energy.
There is a comprehensive literature on seismic processing but to simplify, [1] gives a very good overall review in that domain. There, presentations and comparisons of different techniques for both seismic modeling and imaging can be found. The simulated prestack depth migration process, which is the subject of the present patent, has been developed as an indirect result of studies of the concept of resolution function in seismics ([2],[3],[4],[5]). This function is naturally defined in a specific class of imaging techniques called Generalized Diffraction Tomography ([6], [7], [8]). The latter approach was recently re-programed in terms of local imaging using Fast Fourier Transforms ((F)FT) in wavenumber domains, and illustrated in both seismics and GPR cases ([9], [10], [11], [12], [13]). The simulated prestack local imaging process—hereafter referred to as “SimPLI”—is derived from the local imaging concept for the case where no seismic (or GPR) recordings (synthetic or real) are available. In the following, the seismic domain is used to explain and illustrate the present invention.